Commonsense knowledge is crucial to many natural language processing tasks. Existing works usually incorporate graph knowledge with conventional graph neural networks (GNNs), resulting in a sequential pipeline that compartmentalizes the encoding processes for textual and graph-based knowledge. This compartmentalization does, however, not fully exploit the contextual interplay between these two types of input knowledge. In this paper, a novel context-aware graph-attention model (Context-aware GAT) is proposed, designed to effectively assimilate global features from relevant knowledge graphs through a context-enhanced knowledge aggregation mechanism. Specifically, the proposed framework employs an innovative approach to representation learning that harmonizes heterogeneous features by amalgamating flattened graph knowledge with text data. The hierarchical application of graph knowledge aggregation within connected subgraphs, complemented by contextual information, to bolster the generation of commonsense-driven dialogues is analyzed. Empirical results demonstrate that our framework outperforms conventional GNN-based language models in terms of performance. Both, automated and human evaluations affirm the significant performance enhancements achieved by our proposed model over the concept flow baseline.